4024/22 Oct/Nov 2025, Question 23: Area of a Sector
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 5 marks
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The question, in short
Find what percentage of the large circle's area is shaded, given radii 10 cm and 7 cm, sector angle 130°, and C on the large circle with AC = BC.
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Solution · 5 marks
- 1Sector OAB = 130/360 × π × 7² = 55.58… cm²
- 2Angle COA = angle COB = (360 − 130) ÷ 2 = 115°
- 3Triangles OAC + OBC = 2 × 1/2 × 7 × 10 × sin 115° = 63.44… cm²
- 4Shaded area = 55.58… + 63.44… = 119.03… cm²
- 5Percentage = 119.03… ÷ (π × 10²) × 100 = 37.88… ≈ 37.9%
Answer37.9 or 37.87 to 37.89…
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Also searched as: 4024/22/O/N/25 · 4024_w25_qp_22 · 4024 w25 22 · question 23.
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